How can a 15th century concept inspire modern architecture? - well, there are many ways to interpret it, the most obvious being literall copying of the detailing and patterns. I would like to offer however a different approach.
Lets try to break down what renaissance was at its core, ie what informed its aesthetic. At its core it was a philosophical change resulting in rise of secularism and emergence of the scientific method. The architects challenged the dominant verticals of the gothic style and to emphasise the change they turned to horizontals - thus we have our first principle - strong horizontal lines in the facade.
Interest in mathematics and the natural order created an affinity for emphasising rhythm, often expressed in symmetrical layouts and the arrangement of columns in buildings or upright plants like cypress in gardens. And so our second and third principles is use of symmetry and rhythm.
There have been of course many other characteristic elements regarding ornamentation, levels etc. but to keep our composition streamlined I will stop at the three above.